CNBC's Bob Pisani looks at the day's market action after the closing bell. Materials and financials are among the sectors up more than 2 percent today.

Stocks closed out the session with a sharp bang Thursday, with major averages rallying more than 2 percent across the board, as lawmakers seemed to move closer to a deal to resolve the political stalemate in Washington.

"No one's going to get in the way of this move—we've been up more than 200 points all day so you're going to be hard pressed to find someone on the other side of the trade," said Art Hogan, managing director of Lazard Capital Markets. "This is clearly the light at the end of the tunnel that everyone wants."

The Dow Jones Industrial Average catapulted 323.09 points, or 2.18 percent, to close at 15,126.07. All 30 components in positive territory, propelled by Boeing and UnitedHealth.

The S&P 500 vaulted 36.16 points, or 2.18 percent, to end at 1,692.56. And the Nasdaq shot up 82.97 points, or 2.26 percent, to finish at 3,760.75.

The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, tumbled near 16.

All key S&P sectors closed in positive territory, boosted by financials and industrials. Both sectors had been hit hardest in recent days. Meanwhile, defensive sectors including utilities and telecoms lagged the broader market rally.

"Assuming the market holds on to most of today's gains, I expect some follow-through tomorrow (Friday) that could challenge 1,700 on the S&P 500," according to Elliot Spar, market strategist at Stifel Nicolaus. "Before getting too excited about that move, there will be plenty of overhead supply to get through especially on those big-cap Nasdaq names that have come under pressure this week."

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With earnings season underway, Nick Raich, The Earnings Scout CEO, expects a majority of companies to cut estimates.

And President Barack Obama is willing to look at the proposal to extend the debt ceiling but insists that lawmakers end the government shutdown as well, according to a White House official.

"It is important to remember that the debt ceiling is an arbitrary limit set by Congress—it can be changed at any time and can even be suspended as it was for three months earlier this year," wrote Gary Thayer, chief macro strategist at Wells Fargo Advisors. "Looking back, Congress has always raised the debt ceiling when it was necessary to do so—in fact, Congress has raised the debt ceiling 27 times in the past 40 years. "

President Obama and congressional leaders were set to meet on Thursday for further discussions.

"We've had a situation with a technically oversold market and down nearly 5 percent from 2-1/2 weeks ago… so the market is ripe for a bounce higher," said Randy Frederick, managing director of trading and derivatives with the Schwab Center for Financial Research. "But people are tentative to positive news and things can change very quickly."

The dollar rose to a two-week high against a basket of major currencies. Treasury yields rose to their highest in more than two weeks. Benchmark 10-year notes were last down 12/32 in price to yield 2.71 percent, the highest since September 23.

Meanwhile, the Treasury sold $13 billion in 30-year bonds at a high yield of 3.758 percent. The bid-to-cover ratio, an indicator of demand, was 2.64, versus a recent average of 2.47.

Rep. Brad Sherman, (D-CA), and Rep. Scott Garrett, (R-NJ), weigh in on the ability of President Obama and House Republicans to come to a short-term deal to end the debt crisis.

On the economic front, weekly jobless claims increased six-month high last week, according to the Labor Department, but the underlying trend pointed to a steadily improving labor market. California accounted for half of the increase in claims as the state continued to deal with technical glitches from its computer upgrades. And another portion of the claims were from non-federal workers affected by the government shutdown.

Boeing climbed after Canaccord Genuity started coverage of the Dow component with a "buy" rating and a price target of $140.

Tiffany rallied after Sterne Agee raised its rating on the upscale jewelry retailer to "buy" from "neutral."

BlackBerry rose after co-founder Mike Lazaridis boosted his stake in the troubled smartphone maker to 8 percent and is considering buying the entire company, according to an SEC filing. BlackBerry shares have plunged more than 30 percent year to date.

Bucking the positive trend, Citrix Systems tumbled more than 10 percent to lead the S&P 500 laggards after the software maker estimated quarterly results below current expectations.

San Francisco Fed President John Williams said the central bank will reduce its bond-buying program gradually as the economy continues to improve, based on progress on jobs and inflation.

"This won't be a slamming on the brakes, it will be an easing off the gas," said Williams.

On Wednesday, President Barack Obama officially nominated Federal Reserve Vice Chair Janet Yellen to replace Ben Bernanke as the chairman of the central bank. Yellen is widely perceived as dovish on monetary policy and investors expect her to take a gradual path towards a reduction in the Fed's monthly $85 billion asset purchases.